Question, in a segment of line, how do we define the extremities? I mean, does the line exist at its end? I mean, the separation can't belong to either the line or the space around it, right? if it belongs to the line or the space, I can find another separation point to the right or to the left. But it can't be both space and line.

Wouldn't it depend on whether the points of the set belong to an open or closed (well, actually a compact) set? If it is closed it has definite end points but not if it is open.

If I have 2 numbers and if one of them is rational and the difference between them is rational as well, then the other number is rational, too, right? So, if I take any number and 1 which is a rational number and take the difference between the two and if that difference is rational, the second number is rational. Well, so we can test the difference for rationality the same way we did for the first number, infinitely. If we do this we eventually get a difference of 0, which is rational, so by backpedelling infinitely, we should get that all numbers in that chain are rational.

Well, if I want to test 3 for rationality, I can find the average point between the two and the distance between that average point to 1 and 3. Since we assumed 1 is rational, if the distance from 1 and the average point is rational, then the A.P which is 2 is also rational. and since 2 is rational and the distance from 3 to is rational, then so is 3.
Well, if I want to test e this way, I have no guarantees that the first AP or the first distance are rational (but if one is true, then the other is true, too), but I can test the first ap this way, too, I just find the ap to the first ap, the second ap.
If I do this infinitely, the Aps will grow closer and closer to 1, the distance between them will be zero. Zero's a rational number, which means that the infinieth AP will be rational, so i can test our original number against this AP, the same shit'll happen and if I keep testing the original number against the APs infinitely, I'll eventually hit the original number which will be, therefore, rational.

Well, if I want to test 3 for rationality, I can find the average point between the two and the distance between that average point to 1 and 3. Since we assumed 1 is rational, if the distance from 1 and the average point is rational, then the A.P which is 2 is also rational. and since 2 is rational and the distance from 3 to is rational, then so is 3.
Well, if I want to test e this way, I have no guarantees that the first AP or the first distance are rational (but if one is true, then the other is true, too), but I can test the first ap this way, too, I just find the ap to the first ap, the second ap.
If I do this infinitely, the Aps will grow closer and closer to 1, the distance between them will be zero. Zero's a rational number, which means that the infinieth AP will be rational, so i can test our original number against this AP, the same shit'll happen and if I keep testing the original number against the APs infinitely, I'll eventually hit the original number which will be, therefore, rational.

I don't think I understand how this works.
You have no guarantee that the first ap or distance is rational, but if you've subtracted a rational number from e then the difference is guaranteed to be irrational. The distance between the average point and the rational number is irrational because the average also is irrational.

Can someone tell me how to find the absolute value of a complex number?

A man is dying, and is leaving $2400 to his daughter and her unborn child, of which the sex is unknown, and won't be know until after the man dies.
The man decides these conditions for how the money will be split:
If the baby is a boy, the boy will receive $1600 (2/3) of the money, and the mother will receive the rest (1/3) of the money.
However, if the baby is a girl, the girl will receive $800 (1/3) of the money, and the mother the rest (2/3).
It turns out that the mother had twins, one boy and a girl.
Find out how much money each should get, knowing that the mother will also still receive money.

Looks easy, but it really isn't. (It scared JohnnyMo1 into not talking to me still.)

Looks easy, but it really isn't. (It scared JohnnyMo1 into not talking to me still.)

You could say that the girl = x, the mom = 2x, and the boy = 4x (since the boy gets twice as much as the mom, the mom gets twice as much as the girl), and that totals 7x. Therefore you make it out in sevenths. Boy gets 4/7, mom gets 2/7, and girl gets 1/7.

Something I just noticed about the roots of one.
The square root of one is 1 or -1.
The fourth roots of one are 1,-1,i,-i.
The eighth roots are those previously listed along with both square roots of both positive and negative i.
It would follow that the infinite root of 1 would be a unit circle along the complex plane, and that 1^0 has infinitely many values, amongst them i. The principle value, of course, being one.
Furthermore, any number with an absolute value of x would then equal any point on that circle you take the last root.
Therefore, infinitesimals are baaad and I should stop using them.

The program associates a position vector with a signal strength. The position vector is normalized to a two-dimensional vector (expressed in meters) and the signal strength is normalized to watts.

From my understanding of physics it seems that the signal strength is inversely proportional to the square of the distance. Meaning that for any arbitrary position v, the power is approximately
where x is the location of the source of the signal and k is some constant.

Or equivalently:

Measuring the signal strengths P(v) at multiple different positions v gives me an overdetermined system of polynomial equations (of the second degree).

I've been wanting to learn about how these work, but I haven't finished calculus yet, so I have no idea what's going on

It's just an infinite (theoretically) amount of orthogonal functions that are multiplied by some constant and then added together. With this sum you can create literally any periodic function. It's pretty awesome.

Hey, I am currently in an engineering program and I am having trouble with the math. Specifically getting good at integrals. I have tried learning them from khan academy but they don't seem to help much with the types of problems we get. Is there any really good resource for learning integrals from the very basics to more advanced because i have a month to study before my exam and am really freaking out.

Hey, I am currently in an engineering program and I am having trouble with the math. Specifically getting good at integrals. I have tried learning them from khan academy but they don't seem to help much with the types of problems we get. Is there any really good resource for learning integrals from the very basics to more advanced because i have a month to study before my exam and am really freaking out.

I'm in a sophomore level Intro to Proofs class as a requirement for my recently added math major. Some of the questions asked in there boil my blood. The professor wrote a definition for the least upper bound of a set of real numbers the other day. It was something like "u is an upper bound for set A of reals if u is an upper bound for A and if for every epsilon greater than zero there exists b in A such that b > u - epsilon." Then someone says, "So epsilon has to be zero." The professor says, "No, epsilon is always positive." "So epsilon is a limit?"

Grguhagugughh.

I remember having that kind of trouble in the beginning with epsilon delta stuff. I just expected it to be something it wasn't.

Can someone explain what a "perfect differential" is? It came up in mechanics to show a force is conservative, and my lecturer skipped over it entirely. He wouldn't test it, it's just out of interest's sake. And if it is not immediately obvious from its definition, how would this show a force is conservative if fdr is a perfect differential?

the only method i know (for a 3 by 3) involves calculating the determinants of a bunch of 2 by 2s using its elements, but scaling that up to 5 by 5, that'd be like what, 3600 determinants of 2 by 2 matrices or something?

which would just be silly

Edited:

also please tell me if that statement was just outright dumb, because it's late and i can't ~maths~

Can someone explain what a "perfect differential" is? It came up in mechanics to show a force is conservative, and my lecturer skipped over it entirely. He wouldn't test it, it's just out of interest's sake. And if it is not immediately obvious from its definition, how would this show a force is conservative if fdr is a perfect differential?

I haven't heard it called a perfect differential, but I assume it means that it is path independent. (because of the conservative nature)

Let's say I have a wave pair of arbitrary periodic waves. I draw these inside a modeling program on the sides of a long box running along the positive end of the program's Z axis, and use those to generate one of...these.
First question, what do you call the third (black) wave? Like, what type of wave is it when it's along more than two axes? I only ever dealt with them regarding light polarization before, I don't know the mathematical term.

Anyway, the second question, the real question, is this. Let's say I disable the visibility of the waves on the sides of the box, and leave only the third, black one visible. So, if I'm viewing this box along its Z axis, rotated along the Z axis to see the box only along its X and Z axes, I see the third wave in the shape of the wave drawn on that side of the box. If I rotate it along the Z axis to view only the Y and Z axes, I see the other. But if I view it by some arbitrary rotation about the box's Z axis, I see other two axis waves, which change with the rotation.

How do you define those waves in terms of the two waveforms they are drawn from and the Z axis rotation they are viewed from?

I'm pretty sure that'd be a torsional wave, I imagine you could describe a particle on that wave in cylindrical co-ordinates (and if you wanted convert back to Cartesian). You'd have constant radius, and i think from the other two waves you could figure out its height and a rotation from the origin of theta.

If you were building it out of two sine waves with same speed, angular velocity etc, I'm pretty sure if you're interested about a point on the wave, if it's at height z=k it would stay on that plane, move on a circle with constant radius, with the radius given by the amplitude of one of the 2D waves you're using to describe it, and angle from the point (0,0,k) changing at a constant rate (I think it'd change with the same angluar velocity as the waves). If you wanted to image that wave propagating through space, you'd have a changing z which moves at the same speed as the 2D ones. Then again I've never done waves like this in my life so I might be wrong, this is just what I imagine would happen.